A Hessenberg Markov chain for fast fibre delay line length optimization

In this paper we present an approach to compute the invariant vector of the N + 1 state Markov chain P presented in (Rogiest et al., Lecture Notes in Computer Science, NET-COOP 2007 Special Issue, pp. 4465:185-194) to determine the loss rate of an FDL buffer consisting of N lines, by solving a related Hessenberg system (i.e., a Markov chain skip-free in one direction). This system is obtained by inserting additional time instants in the sample paths of P and allows us to compute the loss rate for various FDL lengths by solving a single system. This is shown to be especially effective in reducing the computation time of the heuristic LRA algorithm presented in (Lambert et al., Proc. NAEC 2005, pp. 545-555) to optimize the FDL lengths, where improvements of several orders of magnitude can be realized

Maximal-entropy random walk unifies centrality measures

In this paper analogies between different (dis)similarity matrices are derived. These matrices, which are connected to path enumeration and random walks, are used in community detection methods or in computation of centrality measures for complex networks. The focus is on a number of known centrality measures, which inherit the connections established for similarity matrices. These measures are based on the principal eigenvector of the adjacency matrix, path enumeration, as well as on the stationary state, stochastic matrix or mean first-passage times of a random walk. Particular attention is paid to the maximal-entropy random walk, which serves as a very distinct alternative to the ordinary random walk used in network analysis. The various importance measures, defined both with the use of ordinary random walk and the maximal-entropy random walk, are compared numerically on a set of benchmark graphs. It is shown that groups of centrality measures defined with the two random walks cluster into two separate families. In particular, the group of centralities for the maximal-entropy random walk, connected to the eigenvector centrality and path enumeration, is strongly distinct from all the other measures and produces largely equivalent results.Comment: 7 pages, 2 figure

Effects of image charges, interfacial charge discreteness, and surface roughness on the zeta potential of spherical electric double layers

We investigate the effects of image charges, interfacial charge discreteness, and surface roughness on spherical electric double layers in electrolyte solutions with divalent counter-ions in the setting of the primitive model. By using Monte Carlo simulations and the image charge method, the zeta potential profile and the integrated charge distribution function are computed for varying surface charge strengths and salt concentrations. Systematic comparisons were carried out between three distinct models for interfacial charges: 1) SURF1 with uniform surface charges, 2) SURF2 with discrete point charges on the interface, and 3) SURF3 with discrete interfacial charges and finite excluded volume. By comparing the integrated charge distribution function (ICDF) and potential profile, we argue that the potential at the distance of one ion diameter from the macroion surface is a suitable location to define the zeta potential. In SURF2 model, we find that image charge effects strongly enhance charge inversion for monovalent interfacial charges, and strongly suppress charge inversion for multivalent interfacial charges. For SURF3, the image charge effect becomes much smaller. Finally, with image charges in action, we find that excluded volumes (in SURF3) suppress charge inversion for monovalent interfacial charges and enhance charge inversion for multivalent interfacial charges. Overall, our results demonstrate that all these aspects, i.e., image charges, interfacial charge discreteness, their excluding volumes have significant impacts on the zeta potential, and thus the structure of electric double layers.Comment: 11 pages, 10 figures, some errors are change

A new mechanism for spatial pattern formation via lateral and protrusion-mediated lateral signalling

Tissue organization and patterning are critical during development when genetically identical cells take on different fates. Lateral signalling plays an important role in this process by helping to generate self-organized spatial patterns in an otherwise uniform collection of cells. Recent data suggest that lateral signalling can be mediated both by junctional contacts between neighbouring cells and via cellular protrusions that allow non-neighbouring cells to interact with one another at a distance. However, it remains unclear precisely how signalling mediated by these distinct types of cell-cell contact can physically contribute to the generation of complex patterns without the assistance of diffusible morphogens or pre-patterns. To explore this question, in this work we develop a model of lateral signalling based on a single receptor/ligand pair as exemplified by Notch and Delta. We show that allowing the signalling kinetics to differ at junctional versus protrusion-mediated contacts, an assumption inspired by recent data which show that the cleavage of Notch in several systems requires both Delta binding and the application of mechanical force, permits individual cells to act to promote both lateral activation and lateral inhibition. Strikingly, under this model, in which Delta can sequester Notch, a variety of patterns resembling those typical of reaction-diffusion systems is observed, together with more unusual patterns that arise when we consider changes in signalling kinetics, and in the length and distribution of protrusions. Importantly, these patterns are self-organizing-so that local interactions drive tissue-scale patterning. Together, these data show that protrusions can, in principle, generate different types of patterns in addition to contributing to long-range signalling and to pattern refinement

Effective zero-thickness model for a conductive membrane driven by an electric field

The behavior of a conductive membrane in a static (DC) electric field is investigated theoretically. An effective zero-thickness model is constructed based on a Robin-type boundary condition for the electric potential at the membrane, originally developed for electrochemical systems. Within such a framework, corrections to the elastic moduli of the membrane are obtained, which arise from charge accumulation in the Debye layers due to capacitive effects and electric currents through the membrane and can lead to an undulation instability of the membrane. The fluid flow surrounding the membrane is also calculated, which clarifies issues regarding these flows sharing many similarities with flows produced by induced charge electro-osmosis (ICEO). Non-equilibrium steady states of the membrane and of the fluid can be effectively described by this method. It is both simpler, due to the zero thickness approximation which is widely used in the literature on fluid membranes, and more general than previous approaches. The predictions of this model are compared to recent experiments on supported membranes in an electric field.Comment: 14 pages, 5 figure

A note on multi-dimensional Camassa-Holm type systems on the torus

We present a $2n$-component nonlinear evolutionary PDE which includes the $n$-dimensional versions of the Camassa-Holm and the Hunter-Saxton systems as well as their partially averaged variations. Our goal is to apply Arnold's [V.I. Arnold, Sur la g\'eom\'etrie diff\'erentielle des groupes de Lie de dimension infinie et ses applications \`a l'hydrodynamique des fluides parfaits. Ann. Inst. Fourier (Grenoble) 16 (1966) 319-361], [D.G. Ebin and J.E. Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid. Ann. of Math. 92(2) (1970) 102-163] geometric formalism to this general equation in order to obtain results on well-posedness, conservation laws or stability of its solutions. Following the line of arguments of the paper [M. Kohlmann, The two-dimensional periodic $b$-equation on the diffeomorphism group of the torus. J. Phys. A.: Math. Theor. 44 (2011) 465205 (17 pp.)] we present geometric aspects of a two-dimensional periodic $\mu$-$b$-equation on the diffeomorphism group of the torus in this context.Comment: 14 page

The importance of XY anisotropy in Sr2IrO4 revealed by magnetic critical scattering experiments

The magnetic critical scattering in Sr$_2$IrO$_4$ has been characterized using X-ray resonant magnetic scattering (XRMS) both below and above the 3D antiferromagnetic ordering temperature, T$_{\text{N}}$. The order parameter critical exponent below T$_{\text{N}}$ is found to be \beta=0.195(4), in the range of the 2D XYh$_4$ universality class. Over an extended temperature range above T$_{\text{N}}$, the amplitude and correlation length of the intrinsic critical fluctuations are well described by the 2D Heisenberg model with XY anisotropy. This contrasts with an earlier study of the critical scattering over a more limited range of temperature which found agreement with the theory of the isotropic 2D Heisenberg quantum antiferromagnet, developed to describe the critical fluctuations of the conventional Mott insulator La$_2$CuO$_4$ and related systems. Our study therefore establishes the importance of XY anisotropy in the low-energy effective Hamiltonian of Sr$_2$IrO$_4$, the prototypical spin-orbit Mott insulator.Comment: 6 pages, 4 figure

Distilling Information Reliability and Source Trustworthiness from Digital Traces

Online knowledge repositories typically rely on their users or dedicated editors to evaluate the reliability of their content. These evaluations can be viewed as noisy measurements of both information reliability and information source trustworthiness. Can we leverage these noisy evaluations, often biased, to distill a robust, unbiased and interpretable measure of both notions? In this paper, we argue that the temporal traces left by these noisy evaluations give cues on the reliability of the information and the trustworthiness of the sources. Then, we propose a temporal point process modeling framework that links these temporal traces to robust, unbiased and interpretable notions of information reliability and source trustworthiness. Furthermore, we develop an efficient convex optimization procedure to learn the parameters of the model from historical traces. Experiments on real-world data gathered from Wikipedia and Stack Overflow show that our modeling framework accurately predicts evaluation events, provides an interpretable measure of information reliability and source trustworthiness, and yields interesting insights about real-world events.Comment: Accepted at 26th World Wide Web conference (WWW-17

On the Nonlocal Equations and Nonlocal Charges Associated with the Harry Dym Hierarchy

A large class of nonlocal equations and nonlocal charges for the Harry Dym hierarchy is exhibited. They are obtained from nonlocal Casimirs associated with its bi-Hamiltonian structure. The Lax representation for some of these equations is also given.Comment: to appear in Journal of Mathematical Physics, 17 pages, Late

Coordinated control of Notch/Delta signalling and cell cycle progression drives lateral inhibition-mediated tissue patterning

Coordinating cell differentiation with cell growth and division is crucial for the successful development, homeostasis and regeneration of multicellular tissues. Here, we use bristle patterning in the fly notum as a model system to explore the regulatory and functional coupling of cell cycle progression and cell fate decision-making. The pattern of bristles and intervening epithelial cells (ECs) becomes established through Notch-mediated lateral inhibition during G2 phase of the cell cycle, as neighbouring cells physically interact with each other via lateral contacts and/or basal protrusions. Since Notch signalling controls cell division timing downstream of Cdc25, ECs in lateral contact with a Delta-expressing cell experience higher levels of Notch signalling and divide first, followed by more distant neighbours, and lastly Delta-expressing cells. Conversely, mitotic entry and cell division makes ECs refractory to lateral inhibition signalling, fixing their fate. Using a combination of experiments and computational modelling, we show that this reciprocal relationship between Notch signalling and cell cycle progression acts like a developmental clock, providing a delimited window of time during which cells decide their fate, ensuring efficient and orderly bristle patterning